Average Error: 0.5 → 0.1
Time: 18.9s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)
double f(double x, double y, double z, double t, double a) {
        double r523167 = 60.0;
        double r523168 = x;
        double r523169 = y;
        double r523170 = r523168 - r523169;
        double r523171 = r523167 * r523170;
        double r523172 = z;
        double r523173 = t;
        double r523174 = r523172 - r523173;
        double r523175 = r523171 / r523174;
        double r523176 = a;
        double r523177 = 120.0;
        double r523178 = r523176 * r523177;
        double r523179 = r523175 + r523178;
        return r523179;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r523180 = 120.0;
        double r523181 = a;
        double r523182 = 60.0;
        double r523183 = z;
        double r523184 = t;
        double r523185 = r523183 - r523184;
        double r523186 = x;
        double r523187 = y;
        double r523188 = r523186 - r523187;
        double r523189 = r523185 / r523188;
        double r523190 = r523182 / r523189;
        double r523191 = fma(r523180, r523181, r523190);
        return r523191;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.5
Target0.2
Herbie0.1
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.5

    \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

  2. Simplified0.5

    \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
  3. Using strategy rm

  4. Applied associate-/l*0.1

    \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right)\]

  5. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60 (/ (- z t) (- x y))) (* a 120))

  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))